Combination of space–time conservation element/solution element method and continuous prediction technique for accelerated simulation of simulated moving bed chromatography

Yao, Chuanyi; Tang, Shaokun; Lu, Yinghua; Yao, Huan; Tade, Moses O.

doi:10.1016/j.cep.2015.07.023

Cited by 8 publications

(5 citation statements)

References 42 publications

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“…Equations (7)–(11) constitute a partial differential equation system that was solved by the space–time conservation element/solution element method 42 . Before solving the model equations, the model parameters, including ε b , D L , k e , and the adsorption isotherms of rebaudioside A and stevioside, must first be determined.…”

Section: Resultsmentioning

confidence: 99%

Using a machine learning model for the optimal design of simulated moving bed processes and its application to separate rebaudioside A and stevioside

Yao

Zheng

Chen

et al. 2021

J of Chemical Tech & Biotech

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BACKGROUND Solving a mechanistic model of simulated moving bed (SMB) is extremely time consuming, therefore, it is inefficient for online control using the optimization method based on such a mechanistic model. To this end, the machine learning model can be regarded as a potential substitution to accelerate the optimization process. RESULTS Several machine learning algorithms were applied to predict the product purities under various operation conditions using two SMB processes as case studies: i.e., a sugar separation of rebaudioside A and stevioside, as well as an enantioseparation of 1,1′‐bi‐2‐naphthol racemate. The results indicate that the random forest (RF) model and the deep neural network (DNN) model provide a satisfactory accuracy with a mean absolute error (MAE) lower than 0.19% (RF) and 0.08% (DNN), respectively. During the optimization process to maximize the feed flowrate under specific purity requirements, among the two selected models, DNN model showed a better generalization ability than RF model and gave a feed flowrate 10% higher than the highest value in the training dataset, which was consistent with the result obtained by using the mechanistic model. The optimized operation conditions for sugar separation were verified experimentally and the achieved purities of rebaudioside A and stevioside were 99.2% and 98.8%, respectively. CONCLUSION The DNN model was successfully used to substitute the mechanistic model to reach a rapid optimization of SMB processes with an improved efficiency of 103 ~ 104 times. © 2021 Society of Chemical Industry (SCI).

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Section: Resultsmentioning

confidence: 99%

Using a machine learning model for the optimal design of simulated moving bed processes and its application to separate rebaudioside A and stevioside

Yao

Zheng

Chen

et al. 2021

J of Chemical Tech & Biotech

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“…Equation 10is the PDE formulation which is solved using the CE/SE method. For the detailed derivation of the CE/SE method, the reader is referred to [12,[17][18][19][20][21]. Here, only the final equations of the fully discretized scheme in space and time are presented.…”

Section: Conservation Element/solution Element (Ce/se) Methodsmentioning

confidence: 99%

“…The different versions of the CE/SE method only differ in the way the spatial derivative u z of the state variables is calculated. In the current work, the proposition of [21] is used.…”

Section: Conservation Element/solution Element (Ce/se) Methodsmentioning

confidence: 99%

“…It was shown [12] that the solutions obtained using the CE/SE method are comparable in accuracy with a MOL approach using a fifth-order high-resolution weighted essentially non-oscillatory (WENO) discretization scheme but need a significantly shorter calculation time. More recently, results were extended in [21] by combining the CE/SE method with a continuous prediction technique. Again, focus was on the mass transfer model for binary SMB processes with linear and nonlinear adsorption isotherms, and again it was shown for a benchmark problem that the CE/SE method is very fast compared to an MOL and a wavelet collocation approach.…”

Section: Introductionmentioning

confidence: 99%

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Efficient Simulation of Chromatographic Processes Using the Conservation Element/Solution Element Method

2020

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Chromatographic separation processes need efficient simulation methods, especially for nonlinear adsorption isotherms such as the Langmuir isotherms which imply the formation of concentration shocks. The focus of this paper is on the space–time conservation element/solution element (CE/SE) method. This is an explicit method for the solution of systems of partial differential equations. Numerical stability of this method is guaranteed when the Courant–Friedrichs–Lewy condition is satisfied. To investigate the accuracy and efficiency of this method, it is compared with the classical cell model, which corresponds to a first-order finite volume discretization using a method of lines approach (MOL). The evaluation is done for different models, including the ideal equilibrium model and a mass transfer model for different adsorption isotherms—including linear and nonlinear Langmuir isotherms—and for different chromatographic processes from single-column operation to more sophisticated simulated moving bed (SMB) processes for the separation of binary and ternary mixtures. The results clearly show that CE/SE outperforms MOL in terms of computational times for all considered cases, ranging from 11-fold for the case with linear isotherm to 350-fold for the most complicated case with ternary center-cut eight-zone SMB with Langmuir isotherms, and it could be successfully applied for the optimization and control studies of such processes.

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“…Numerical solutions can be an alternative to the theoretical algebraic solutions, to constitute the chromatograms of various network configurations, to calculate the performance indicators, to search for the optimum flowrates and switching time (Rodrigues et al, 2007;Agrawal & Kawajiri, 2012;Nowak et al, 2012;Wu et al, 2013;Li et al, 2014a,b;Bentley et al, 2014;Sreedhar et al, 2014;Yao et al, 2015;Yu et al, 2015). Numerical solutions of different column models with various adsorption isotherms have been investigated (Dünnebier et al, 2000).…”

Section: Introductionmentioning

confidence: 99%

Bayesian inference based process design and uncertainty analysis of simulated moving bed chromatographic systems

He,

Zhao

2019

Preprint

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Prominent features of simulated moving bed (smb) chromatography processes in the downstream processing is based on the determination of operating conditions. However, effects of different types of uncertainties have to be studied and analysed whenever the triangle theory or numerical optimization approaches are applied. In this study, a Bayesian inference based method is introduced to consider the uncertainty of operating conditions on the performance assessment, of a glucose-fructose smb unit under linear condition. A multiple chain Markov Chain Monte Carlo (mcmc) algorithm (i.e., Metropolis algorithm with delayed rejection and adjusted Metropolis) is applied to generate samples. The proposed method renders versatile information by constructing from the mcmc samples, e.g., posterior distributions, uncertainties, credible intervals of the operating conditions, and posterior predictive check and Pareto fronts between each pair of the performance indicators. Additionally, the mcmc samples can be mapped onto the (mII, mIII) and (mIV, mI) planes to show the actually complete separation region under uncertainties. The proposed method is a convenient tool to find both optimal values and uncertainties of the operating conditions. Moreover, it is not limited to smb processes under the linear isotherm; and it should be more powerful in the nonlinear scenarios.

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Combination of space–time conservation element/solution element method and continuous prediction technique for accelerated simulation of simulated moving bed chromatography

Cited by 8 publications

References 42 publications

Using a machine learning model for the optimal design of simulated moving bed processes and its application to separate rebaudioside A and stevioside

Using a machine learning model for the optimal design of simulated moving bed processes and its application to separate rebaudioside A and stevioside

Efficient Simulation of Chromatographic Processes Using the Conservation Element/Solution Element Method

Bayesian inference based process design and uncertainty analysis of simulated moving bed chromatographic systems

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